Converting [A] into [C] is called:

The correct option is Hoffmann Degradation Reaction.

Let's understand the chemistry behind this conversion step-by-step:

1. Understanding the Hoffmann Degradation Reaction:
The Hoffmann bromamide degradation reaction (also known as the Hoffmann degradation) is a classic organic reaction used to convert a primary amide into a primary amine with one fewer carbon atom. The general representation of this reaction is:

$$R-CON{H}_2+B{r}_2+4KOH\to R-N{H}_2+K_{2}C{O}_3+2KBr+2H_{2}O$$

2. Why it is called a "Degradation" reaction:
During this reaction, the carbonyl carbon (C=O) of the starting amide is lost as a carbonate ion ($C{O}_3^{2-}$). As a result, the product amine contains one less carbon atom than the starting amide, which explains the term "degradation".

3. Comparing the Options:
- Ammonolysis: This refers to the cleavage of a chemical bond by reaction with ammonia (e.g., converting alkyl halides to amines).
- Hoffmann Degradation Reaction: This is the correct reaction for converting an amide [A] to a primary amine [C] with loss of a carbon atom.
- Carbylamine reaction: This is a test for primary amines where they react with chloroform and potassium hydroxide to form foul-smelling isocyanides.
- Gabriel phthalimide reaction: This is a method used for the preparation of primary alkyl amines from phthalimide, not for converting a simple amide to an amine with carbon chain shortening.